Infection of Novel Coronavirus 2019 (COVID-19) on lung cells and human respiratory systems have raised real concern to the human lives during the current pandemic spread across the world. Recent observations on CT images of human lungs infected by COVID-19 is a challenging task for the researchers in finding suitable image patterns for automatic diagnosis. In this paper, a novel semi-supervised shallow learning network model comprising Parallel Quantum-Inspired Self-supervised Network (PQIS-Net) with Fully Connected (FC) layers is proposed for automatic segmentation followed by patch-based classifications on segmented lung CT images for the diagnosis of COVID-19 disease. The PQIS-Net model is incorporated for fully automated segmentation of lung CT scan images obviating pre-trained convolutional neural network models for feature learning. The PQIS-Net model comprises a trinity of layered structures of quantum bits inter-connected through rotation gates using an 8-connected second-order neighborhood topology for the segmentation of wide variation of local intensities of the CT images. Intensive experiments have been carried out on two publicly available lung CT image data sets thereby achieving promising segmentation outcome and diagnosis efficiency (F1-score and AUC) while compared with the state of the art pre-trained convolutional based models.